of Microprocessors

DIGITAL TONE GENERATION TECHNIQUES 479
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FUND
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Fig. 13-32. (A) Spectrum of Fig. 13-31G as input amplitude varies. (8)
Spectrum of Fig. 13-31H as input amplitude varies. (C) Spectrum
of Fig. 13-311 as input amplitude varies. (0) Spectrum of Fig.
13-31J as input amplitude varies. (E) Spectrum of Fig. 13-31 K as
input amplitude varies.
input amplitude is reduced, which is exactly how most conventional musical
instruments operate. A trumpet played softly, for example, has weaker upper
harmonics than one played loudly. A plucked string's high harmonics decay
more quickly than the fundamental and lower harmonics. Thus, a relatively
realistic simulation can often be obtained simply by applying the amplitude
envelope before the nonlinear shaping operation. It will usually also have to be
applied again afterwards ifChebyshev polynomials are used, since the output
amplitude may not begin to decline until the input amplitude is quite small.
Figure 13-32A-E illustrates this effect using the nonlinear functions given
in Fig. 13-31G-K, respectively. The graphs show the changing waveshape
and how the amplitude (on the Y axis) of each harmonic varies as the input
amplitude (on the X axis) varies. Note the extremely complex, although
definitely structured, harmonic evolution pattern in Fig. 13-32E. For the
patterns to show up, it was necessary to plot the fundamental at one-quarter
of its true amplitude and also show only the first 16 harmonics. Using an
interactive program in which transfer curves can be drawn with a digitizer or
light pen should be exciting to say the least.